Time evolution of a single-spin model coupled to a harmonic oscillator via the method of Mori

1983 ◽  
Vol 61 (11) ◽  
pp. 1475-1478 ◽  
Author(s):  
A. S. T. Pires ◽  
M. E. de Gouvea
Keyword(s):  
Harmonic Oscillator ◽  
Formal Analysis ◽  
Memory Function ◽  
Transverse Field ◽  
Spin Model ◽  
Single Spin ◽  
Complex Models ◽  
Physical Insight ◽  
Time Dependent Behaviour ◽  
Dependent Behaviour

We use Mori's memory function method for coupled operators to calculate the time-dependent behaviour of a single-spin model coupled to a harmonic oscillator. This model enables us to carry out the formal analysis of Mori exactly and gives us the physical insight required to treat more complex models, such as the Ising model in a transverse field coupled to phonons.

Time evolution, relaxation function, and random force for a single-spin model via the method of Mori

1983 ◽  
Vol 61 (3) ◽  
pp. 428-433 ◽  
Author(s):  
M. Howard Lee
Keyword(s):  
Time Evolution ◽  
Relaxation Function ◽  
Memory Function ◽  
Random Force ◽  
Spin Model ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Single Spin ◽  
Dependent Behavior ◽  
Insight Into

We introduce a single-spin model defined by the Hamiltonian H = aSz + bSx, where a and b are constants and Sx and Sz are the x- and z-components of the spin [Formula: see text] operator. We obtain for this model the time-dependent behavior exactly and completely via the method of Mori. To gain an insight into the quantum mechanical mechanisms of time evolution, we make a comparison with Brownian motion by deducing a number of Brownian analogs. Brownian analogs include the spin memory function as well as the random force and its power spectrum.

Application of shotcrete constitutive model to the time dependent behavior of TBM tunnel lining

2018 ◽  
Vol 7 (3) ◽  
pp. 1826
Author(s):  
Heyam H. Shaalan ◽  
Mohd Ashraf Mohamad Ismail ◽  
Romziah Azit
Keyword(s):  
Constitutive Model ◽  
Steel Fibre ◽  
Tunnel Lining ◽  
Time Dependent ◽  
Elastic Behaviour ◽  
Elastic Analysis ◽  
Time Dependent Behaviour ◽  
Shotcrete Lining ◽  
Creep And Shrinkage ◽  
Dependent Behaviour

Shotcrete is ordinary concrete applied to the surface under high pressure. It demonstrates a highly time-dependent behaviour after few hours of application. Traditional approaches assume a simple linear elastic behaviour using a hypothetical young modulus to investigate the time-dependency and creep effects. In this paper, a new constitutive model of shotcrete is applied to evaluate the time-dependent behaviour of a TBM tunnel lining and investigate the parameters that can influence this behaviour. The Shotcrete model is based on the framework of Elasto-plasticity and designed to model shotcrete linings more realistically. The basic data of Pahang-Selangor Raw Water Transfer Project is used for the analysis study. An attempt is made to investigate the influence of some input parameters of the shotcrete model on the time-dependent behaviour of the shotcrete lining. These parameters include the time-dependent stiffness/strength parameters, creep and shrinkage parameters and steel fibre parameters. The variation in shotcrete strength classes causes a noticeable influence on the development of shotcrete compressive strength with time, particularly during the first days of application. The creep and shrinkage strain cause a considerable reduction in the development of the shotcrete stress with time. The impact of steel fibre content is determined, and the result indicated that the development of plain shotcrete stresses with time is lower than that of the reinforced shotcrete. In addition, a comparison study is performed to analyse the tunnel lining behaviour using both shotcrete model and an elastic analysis. Significant differences in shotcrete lining stresses are achieved when using the elastic analysis while the shotcrete model results in a reasonable result that can be used for the design requirements. 

scholarly journals Application of micro-computer tomography and inverse finite element analysis for characterizing the visco-hyperelastic response of bulk liver tissue using indentation

2021 ◽  
Vol 3 (5) ◽  
Author(s):  
Rajeswara R. Resapu ◽  
Roger D. Bradshaw
Keyword(s):  
Finite Element ◽  
Liver Tissue ◽  
Loading Rate ◽  
Time Dependent ◽  
Nonlinear Material ◽  
Computational Time ◽  
List Type ◽  
Prony Series ◽  
Time Dependent Behaviour ◽  
Dependent Behaviour

Abstract In-vitro mechanical indentation experimentation is performed on bulk liver tissue of lamb to characterize its nonlinear material behaviour. The material response is characterized by a visco-hyperelastic material model by the use of 2-dimensional inverse finite element (FE) analysis. The time-dependent behaviour is characterized by the viscoelastic model represented by a 4-parameter Prony series, whereas the large deformations are modelled using the hyperelastic Neo-Hookean model. The shear response described by the initial and final shear moduli and the corresponding Prony series parameters are optimized using ANSYS with the Root Mean Square (RMS) error being the objective function. Optimized material properties are validated using experimental results obtained under different loading histories. To study the efficacy of a 2D model, a three dimensional (3D) model of the specimen is developed using Micro-CT of the specimen. The initial elastic modulus of the lamb liver obtained was found to 13.5 kPa for 5% indentation depth at a loading rate of 1 mm/sec for 1-cycle. These properties are able to predict the response at 8.33% depth and a loading rate of 5 mm/sec at multiple cycles with reasonable accuracy. Article highlights The visco-hyperelastic model accurately models the large displacement as well as the time-dependent behaviour of the bulk liver tissue. Mapped meshing of the 3D FE model saves computational time and captures localized displacement in an accurate manner. The 2D axisymmetric model while predicting the force response of the bulk tissue, cannot predict the localized deformations.

Determination of the Internal Electric Field in the Electrooptic Active Layer of Multilayer Polymer Stacks

1997 ◽  
Vol 488 ◽  
Author(s):  
S. Grossmann ◽  
T. Weyrauch ◽  
W. Haase
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Time Dependent ◽  
Polymer Interfaces ◽  
Internal Electric Field ◽  
Inhomogeneous Distribution ◽  
Time Dependent Behaviour ◽  
Dependent Behaviour

AbstractWe report on a method to investigate the inhomogeneous distribution of an electric dc field in multilayer polymer stacks. In situ electroabsorption (EA) measurements are applied in order to estimate the local electric fields in double layer polymer films. The observed time dependent behaviour is compared with a model equivalent circuit. The results indicate that besides the relation of ohmic resistivities and capacities of the different polymer layers in the investigated systems also the influence of the electric properties of polymer/electrode and polymer/polymer interfaces must be considered.

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